五年级奥数分数裂项试题

2026年09月17日 11:55

有5个网友回答

网友（1）：

从后面往前一步步加
(47x46x...x2)/(52x51x...x6) + (47x46x...x1)/(52x51x...x5) = (47x46x...x2)/(52x51x...x6) x (1+1/5) = (47x46x...x2)/(52x51x...x6) x 6/5
(47x46x...x3)/(52x51x...x7) + (47x46x...x2)/(52x51x...x6) x 6/5 = (47x46x...x3)/(52x51x...x7) x (1 + 2/6 x 6/5) = (47x46x...x3)/(52x51x...x7) x (1 + 2/5) = (47x46x...x3)/(52x51x...x7) x 7/5
(47x46x...x4)/(52x51x...x8) + (47x46x...x3)/(52x51x...x7) x 7/5 = (47x46x...x4)/(52x51x...x8) x (1 + 3/7 x 7/5) = (47x46x...x4)/(52x51x...x8) x (1 + 3/5) = (47x46x...x4)/(52x51x...x8) x 8/5
依此类推
原式=1/52 + 47/(52x51) x (1 + 46/5) = 1/52 + 47/(52x51) x 51/5 = 1/52 + 47/(52x5) = 1/5

网友（2）：

a1=(1/52)(47/51)***(3/7)(2/6)(1/5) S1=a1=(1/5)a2
a2=(1/52)(47/51)***(3/7)(2/6) S2=a2*(1/5)+a2=(6/5)a2=(2/5)a3
a3=(1/52)(47/51)***(3/7) S3=(2/5)a3+a3=(7/5)a3=(3/5)a4
...
an=(1/52)*(47/51)***(n/(n+4)) Sn=(n/5)a(n+1) (n<=47) (此即归纳法)
a47=(1/52)*(47/51) S47=(47/5)a48=(47/5)(1/52)
S48=(47/5)(1/52)+1/52=(52/5)(1/52)=1/5

网友（3）：

您好！很高兴认识你！这道题的答案是1.望采纳

网友（4）：

网友（5）：

one。。。